Question

(1/4)^4/(1/3)^4+(-1/2)^3
please answer this question ​

Answer 1

Step-by-step explanation:

Given :-

(1/4)⁴ ÷ (1/3)⁴ + (-1/2)³

To find :-

Simplify the expression ?

Solution :-

Given expression is

(1/4)⁴ ÷ (1/3)⁴ + (-1/2)³

By Using BODMAS rule

We have to do division first

=> [(1/4)⁴ ÷ (1/3)⁴ ]+ (-1/2)³

=> [(1/4)⁴ / (1/3)⁴ ]+ (-1/2)³

=> [(1/4)⁴× (3/1)⁴ ]+ (-1/2)³

=> [(3)⁴/(4)⁴]+(-1/2)³

=> (3/4)⁴+(-1/2)³

Since (a/b)^m = a^m / b^m

=> [(3×3×3×3)/(4×4×4×4)] + [(-1/2)×(-1/2)×(-1/2)]

=> (81/256)+(-1/8)

LCM of 256 and 8 = 256

=> (81-32)/256

=> 49/256 or

=> 7²/16²

=> (7/16)²

Answer :-

The value of the given expression is (7/16)² or 49/256

Used formulae:-

→ BODMAS rule

→ (a/b)^m = a^m / b^m